Breit-Pauli R-matrix Research Articles

Energy levels and characteristic features in photoionization of Cl III using the R-matrix method

We report study of Cl III for its large number of fine structure bound levels, 890, with n ≤ 10 and l ≤ 9, and 1/2 ≤ j ≤ 19/2 of even and odd parities with spectroscopic designation and photoionization cross sections (σPI) of the levels revealing various characteristic features. Various resonant structures and the shapes of the background, and their interference in σPI are illustrated for the ground, excited equivalent electron, low and high lying excited levels with single valence electron, and effects of fine structure couplings. σPI of the ground level shows Rydberg series of resonances on smooth background, and of equivalent electron levels producing strong closely spaced Rydberg series of resonances belonging to the low lying core ion excitation thresholds. They will impact applications in low temperature plasma. For the single valence electron excited levels, we find that σPI of low lying excited states are dominated by Rydberg series of resonances and of high lying excited states exhibit prominent broad feature of Seaton resonances. Partial photoionization cross sections of the ground level for leaving the core ion in the ground and various excited levels are also presented for applications in plasma modeling. The study was carried out in relativistic Breit–Pauli R-matrix method using a large close coupling wave function expansion of 45 levels of the core ion configurations 3 s23 p2, 3 s3 p3, 3 s23 p3 d, 3 s23 p4 s, 3 s3 p23 d, and 3 p4 with closed 1s, 2s, 2p orbitals. They belong to the optimized set of 13 configurations of Cl IV, 3 s23 p2, 3 s3 p3, 3 s23 p3 d, 3 s23 p4 s, 3 s23 p4 p, 3 s23 p4 d, 3 s3 p23 d, 3 s3 p24 s, 3 s3 p24 p, 3 p4, 3 p33 d, 3 p34 s, and 3 p34 p. Cl III energies are in good agreement with measured values. σPI features of low lying levels were benchmark with observation carried out at Advanced Light Source at LBNL with very good agreement. The present set of high accuracy data should complete for any practical applications.

Atomic structure, electron-impact excitation and collisional-radiative modelling for Ar II

The spectra from singly ionized argon Ar II has significant diagnostic capability in the characterization and modelling of both magnetically-confined fusion and astrophysical plasmas. The literature has several pre-existing data sets for Ar+ but this paper presents the results from 3 new atomic structure and electron-impact scattering models in order to better constrain the differences in atomic data and how they impact well-known plasma diagnostics. Several independent atomic structure methodologies are employed to calculate the energy levels and transition probabilities for each model. The first approach employs a relativistic Dirac–Coulomb Hamiltonian model, the second approach uses a semi-relativistic Breit–Pauli Hamiltonian with the mass-velocity, Darwin and spin–orbit corrections, and in a third case an ICFT approach. Three atomic structure models provide a foundation for Dirac R-matrix, a semi-relativistic ICFT (Intermediate Coupling Frame Transformation) and a Breit–Pauli R-Matrix with Pseudostates (BPRMPS) calculation. Synthetic spectra utilizing these three data sets are compared against measurements taken at the Compact Toroidal Hybrid (CTH) stellarator, and the total radiative power loss is also benchmarked against previous calculations.

R-matrix calculations for opacities: IV. Convergence, completeness, and comparison of relativistic R-matrix and distorted wave calculations for Fe xvii and Fe xviii

To investigate the completeness of coupled channel (CC) Breit–Pauli R-matrix (BPRM) calculations for opacities we employ the relativistic distorted wave (RDW) method to complement (‘top-up’) and compare the BPRM photoionization cross sections for high- nℓ levels of both Fe xvii and Fe xviii . Good agreement is found with background photoionization cross sections using these two methods, which also ensures the correct matching of bound level cross sections for completeness. In order to top-up the CC-BPRM calculations, bound–bound transitions involving additional bound levels, and a large number of doubly-excited quasi-bound levels corresponding to BPRM autoionizing resonances described in the paper RMOPII are calculated using the RDW method. Photoionization cross sections in the high energy region are also computed and compared up to about 500 Ry, and contributions from higher core level excitations than BPRM are considered. The effect of configuration interaction is investigated, which plays a significant role in correctly reproducing some background cross sections. Due to the fact that the additional RDW levels correspond to high- nℓ bound levels that are negligibly populated according to the Mihalas–Hummer–Däppen equation-of-state (paper I), the effect on opacities is expected to be small.

R-Matrix calculations for opacities: II. Photoionization and oscillator strengths of iron ions Fe xvii, Fe xviii and Fe xix

Iron is the dominant heavy element that plays an important role in radiation transport in stellar interiors. Owing to its abundance and large number of bound levels and transitions, iron ions determine the opacity more than any other astrophysically abundant element. A few iron ions constitute the abundance and opacity of iron at the base of the convection zone (BCZ) at the boundary between the solar convection and radiative zones and are the focus of the present study. Together, Fe xvii, Fe xviii and Fe xix represent 85% of iron ion fractions, 20%, 39% and 26% respectively, at the BCZ physical conditions of temperature T ∼ 2.11×106 K and electron density Ne = 3.1×1022 c.c. We report the most extensive R-matrix atomic calculations for these ions for bound–bound and bound–free transitions, the two main processes of radiation absorption. We consider wavefunction expansions with 218 target or core ion fine structure levels of Fe xviii for Fe xvii, 276 levels of Fe xix for Fe xviii, in the Breit–Pauli R-matrix (BPRM) approximation, and 180 LS terms (equivalent to 415 fine structure levels) of Fe xx for Fe xix calculations. These large target expansions, which include core ion excitations to n = 2,3,4 complexes, enable accuracy and convergence of photoionization cross sections, as well as the inclusion of high lying resonances. The resulting R-matrix datasets include 454 bound levels for Fe xvii, 1,174 levels for Fe xviii, and 1,626 for Fe xix up to n⩽ 10 and l = 0–9. Corresponding datasets of oscillator strengths for photoabsorption are: 20 951 transitions for Fe xvii, 141 869 for Fe xviii, and 289 291 for Fe xix. Photoionization cross sections have been obtained for all bound fine structure levels of Fe xvii and Fe xviii, and for 900 bound LS states of Fe xix. Selected results demonstrating prominent characteristic features of photoionization are presented, particularly the strong Seaton photoexcitation-of-core resonances formed via high-lying core excitations with Δn=1 that significantly impact bound–free opacity.

R-matrix calculations for opacities: III. Plasma broadening of autoionizing resonances

A general formulation is employed to study and quantitatively ascertain the effect of plasma broadening of intrinsic autoionizing (AI) resonances in photoionization cross sections. In particular, R-matrix data for iron ions described in the previous paper in the RMOP series (RMOP-II, hereafter RMOP2) are used to demonstrate underlying physical mechanisms due to electron collisions, ion microfields (Stark), thermal Doppler effects, core excitations, and free–free transitions. Breit–Pauli R-matrix cross sections for a large number of bound levels of Fe ions are considered, 454 levels of Fe XVII, 1184 levels of Fe XVIII and 508 levels of Fe XIX. Following a description of theoretical and computational methods, a sample of results is presented to show significant broadening and shifting of AI resonances due to extrinsic plasma broadening as a function of temperature and density. The redistribution of AI resonance strengths broadly preserves their integrated strengths as well as the naturally intrinsic asymmetric shapes of resonance complexes which are broadened, smeared and flattened, eventually dissolving into the bound-free continua.

R-matrix calculations for opacities: I. Methodology and computations

An extended version of the R-matrix methodology is presented for calculation of radiative parameters for improved plasma opacities. Contrast and comparisons with existing methods primarily relying on the distorted wave approximation are discussed to verify accuracy and resolve outstanding issues, particularly with reference to the opacity project (OP). Among the improvements incorporated are: (i) large-scale Breit–Pauli R-matrix calculations for complex atomic systems including fine structure, (ii) convergent close coupling wave function expansions for the (e + ion) system to compute oscillator strengths and photoionization cross sections, (iii) open and closed shell iron ions of interest in astrophysics and experiments, (iv) a treatment for plasma broadening of autoionizing resonances as function of energy-temperature-density dependent cross sections, (v) a ‘top-up’ procedure to compare convergence with R-matrix calculations for highly excited levels, and (vi) spectroscopic identification of resonances and bound (e + ion) levels. The present R-matrix monochromatic opacity spectra are fundamentally different from OP and lead to enhanced Rosseland and Planck mean opacities. An outline of the work reported in other papers in this series and those in progress is presented. Based on the present re-examination of the OP work, opacities of heavy elements might require revisions in high temperature-density plasma sources.

New atomic data for C i Rydberg states compared with solar UV spectra

ABSTRACT We use the Breit–Pauli R-matrix method to calculate accurate energies and radiative data for states in C i up to n = 30 and with l ≤ 3. We provide the full data set of decays to the five 2s2 2p2 ground configuration states 3P0,1,2, 1D2, and 1S0. This is the first complete set of data for transitions from n ≥ 5. We compare oscillator strengths and transition probabilities with the few previously calculated values for such transitions, finding generally good agreement (within 10 per cent) with the exception of values recently recommended by National Institute of Standards and Technology, where significant discrepancies are found. We then calculate spectral line intensities originating from the Rydberg states using typical chromospheric conditions and assuming local thermal equilibrium, and compare them with well-calibrated Solar and Heliospheric Observatory Solar Ultraviolet Measurements of Emitted Radiation ultraviolet (UV) spectra of the quiet Sun. The relative intensities of the Rydberg series are in excellent agreement with observation, which provides firm evidence for the identifications and blends of nearly 200 UV lines. Such comparison also resulted in a large number of new identifications of C i lines in the spectra. We also estimate optical depth effects and find that these can account for much of the absorption noted in the observations. The atomic data can be applied to model a wide range of solar and astrophysical observations.

Biosignature line ratios of [P ii] in exoplanetary and nebular environments

ABSTRACT Being the backbone element of deoxyribonucleic acid, phosphorus is a key component in the search for life in the Universe. To aid in its detection, we present line emissivity ratios for the five lowest-lying forbidden [P ii] transitions, namely those among the levels 3s23p2(3P0, 3P1, 3P2, 1D2, and 1S0). The wavelengths range between 0.44 and 70 µm, and several lie within the spectroscopic domain observable with the JWST. These line ratios have been calculated using a new collisional-radiative-cascade (CRR) model combining calculated collision strengths and level-specific recombination rate coefficients, with both data sets computed using the accurate Breit–Pauli R-matrix method. The CRR model includes a new scheme for (e + ion) recombination to emission-line formation. We compare its effect to models incorporating only electron-impact excitation and spontaneous radiative decay. We find that (e + ion) recombination has a significant impact on all line ratios, and represents a major improvement in physical accuracy of emission-line models.

Experimental and Theoretical Study of Photoionization of Cl III

Photoionization of Cl III ions into Cl IV was studied theoretically using the ab initio relativistic Breit–Pauli R-matrix (BPRM) method and experimentally at the Advanced Light Source (ALS) synchrotron at the Lawrence Berkeley National Laboratory. A relative-ion-yield spectrum of Cl IV was measured with a photon energy resolution of 10 meV. The theoretical study was carried out using a large wave-function expansion of 45 levels of configurations 3s23p2, 3s3p3, 3s23p3d, 3s23p4s, 3s3p23d, and 3p4. The resulting spectra are complex. We have compared the observed spectrum with photoionization cross sections (σPI) of the ground state 3s23p3(4S3/2o) and the seven lowest excited levels 3s23p3(2D5/2o), 3s23p3(2D3/2o), 3s23p3(2P3/2o), 3s23p3(2P1/2o), 3s3p4(4P5/2), 3s3p4(4P3/2) and 3s3p4(4P1/2) of Cl III, as these can generate resonances within the energy range of the experiment. We were able to identify most of the resonances as belonging to various specific initial levels within the primary Cl III ion beam. Compared to the first five levels, resonant structures in the σPI of excited levels of 3s3p4 appear to have a weaker presence. We have also produced combined theoretical spectra of the levels by convolving the cross sections with a Gaussian profile of experimental width and summing them using statistical weight factors. The theoretical and experimental features show good agreement with the first five levels of Cl III. These features are also expected to elucidate the recent observed spectra of Cl III by Sloan Digital Scan Survey project.

Effective Collision Strengths and Radiative Parameters for Lines in the Sc ii Spectrum

Abstract This work reports large-scale calculations of electron excitation effective collision strengths and transition rates for a wide range of Sc ii spectral lines for astrophysical analysis and modeling. The present results are important for reliable abundance determinations in various astrophysical objects, including metal-poor stars, H ii regions, and gaseous nebulae. Accurate descriptions of the target wave functions and adequate accounts of the various interactions between the target levels are of primary importance for calculations of collision and radiative parameters. The target wave functions have been determined by a combination of the multiconfiguration Hartree–Fock and B-spline box-based close-coupling methods, together with the nonorthogonal orbitals technique. The calculations of the collision strengths have been performed using the B-spline Breit–Pauli R-matrix method. The close-coupling expansion includes 145 fine-structure levels of Sc ii belonging to the terms of the 3p 63d 2, 3p 63d4l (l = 0–3), 3p 63d5l (l = 0–3), 3p 63d6s, 3p 64s 2, 3p 64s4l (l = 0–3), 3p 64s5l (l = 0–1), and 3p 64p 2 configurations. The effective collision strengths are reported as a function of electron temperature in the range from 103 to 105 K. The collision and radiative rates are reported for all of the possible transitions between the 145 fine-structure levels. Striking discrepancies exist with the previous R-matrix calculations of the effective collision strengths for the majority of the transitions, indicating possible systematic errors in these calculations. Thus, there is a need for accurate calculations to reduce the uncertainties in the atomic data. The likely uncertainties in our effective collision strengths and radiative parameters have been assessed by means of comparisons with other collision calculations and available experimental radiative parameters.

Inner-shell photoionization of free and confined Mg in the region of the 2p thresholds

Photoionization of the free and confined Mg (Mg@C60) have been calculated in the vicinity of the inner-shell 2p thresholds using R-matrix at the Breit–Pauli R-matrix level with a particular emphasis on the various resonance series leading up to the two lowest inner-shell thresholds and the changes resulting from the confinement. For free Mg, the calculated resonance positions agree well with NIST values, and a number of new resonances are identified. For confined Mg, the calculation was done for various depths of the confining potential well in order to follow the trajectories of the resonances as a function of well depth. The results for the well depth corresponding to Mg@C60 showed that most of the resonances moved to higher photon energy, as a result of the confinement, but a few moved to lower energies. This phenomenology was found to result from the fact that the 3p, 3d and 4s excitations are trapped by the confining potential well, while the higher excitations were not.

Electron impact excitation of Na-like Cu XIX using the Breit–Pauli R-matrix method

Electron impact excitation of Na-like Cu XIX using the Breit–Pauli R-matrix method

Transition Probabilities and Collision Strengths for Fine-structure Levels Excitation of Ti II

Abstract Several spectral features from the stellar and nebular objects arise due to the iron-peak Ti II fine-structure excitations. Transition probabilities and electron excitation collision strengths of iron-peak elements are important for a meaningful interpretation and analysis of the observed astrophysical spectra. Accurate description of atomic structure with open 3d-shell elements is the key to the reliable and accurate computation of radiative and collision rates. The term-dependent one-electron orbitals in the multiconfiguration Hartree–Fock approach with adjustable configuration expansions and semi-empirical fine-tuning for energy corrections have been used in achieving highly accurate target description. A total of 314 Ti II fine-structure levels of the ground 3d 24s and excited 3d 3, 3d4s 2, 3d 24p, 3d 25s, 3d4s4p, 3d 24d, 3d 25p, and 3d 24f configurations have been included in the calculations of these atomic parameters. The present calculation of collision strengths has been performed in a close-coupling approximation based on the B-spline Breit–Pauli R-matrix method with inclusion of spin–orbit interaction term in the Hamiltonian matrices. Effective collision strengths over a Maxwellian distribution of electron velocities at temperatures in the range from 103 to 105 K have been reported for transitions between the 314 fine-structure levels. These wide array of transitions give rise to many main Ti II infrared, optical, and ultraviolet lines from a variety of astrophysical objects. Our calculated parameters are compared with the available other theoretical and experimental results, and through this comparison likely uncertainties in our results have been estimated, especially for transitions among the low-lying fine-structure levels of astrophysical importance.

Photoionization features of the ground and excited levels of Cl II and benchmarking with experiment

This report presents i) various characteristic features in photoionization cross sections (σPI) of Cl II + hν → Cl III + e for many fine structure levels of Cl II, 392 in total with n ≤ 10 and l ≤ 9, ii) comparison of features with those observed in an experiment carried out at the Advanced Light Source at Lawrence Berkeley National Lab, and iii) partial photoionization cross sections of the ground level for ionization leaving the core ion in to various excited levels for applications in plasma modeling. The features correspond to resonant structures, the shape of the background, and their interference effect in σPI of this near neutral ion Cl II with 16 electrons. σPI for the 5 levels of the ground configuration 3s23p4(3P0,1,2, 1D2, 1S0) of Cl II show regions of narrow Rydberg resonances at and near threshold energies, and resonant structures at higher energies in contrast to typical smooth decrease in the background. Various other features in σPI of levels of excited equivalent electron states and broad Seaton resonances in single valence electron excited levels are illustrated with examples. Comparison of calculated σPI of the 15 lowest levels with the combined features of the measured photoionization spectrum shows excellent agreement by reproducing and thus identifying them to the levels that they belong to. The calculations were carried out in relativistic Breit-Pauli R-matrix (BPRM) method using a close coupling wave function expansion of 45 levels up to 4s of the core ion Cl III. These levels were optimized using a set of 12 configurations going up to orbital 5s, 3s23p3, 3s3p4, 3p5, 3s23p23d, 3s23p24s, 3s23p24p, 3s23p24d, 3s23p24f, 3s23p25s, 3s3p33d, 3s23p3d2, 3p43d producing 283 levels of Cl III. The autoionizing resonances are delineated with a fine energy mesh to observe the fine structure effects. The present results will provide high precision parameters for various applications involving this less studied ion.

Breit–Pauli R-Matrix approach for the time-dependent investigation of ultrafast processes

We have refactored the Breit–Pauli R-Matrix integral package within the RMatrxI package to employ a B-Spline basis to allow for level-resolved time-dependent R-Matrix calculations involving a laser pulse. The B-Spline approach independently verifies the accuracy of the current integral package pstg1r.f, but requires greater flexibility at the R-Matrix boundary when describing the continuum wavefunctions. This adaptation can be integrated with either the subsequent serial or parallel Breit–Pauli suite of codes. Program summaryProgram Title: BSplineStg1Program Files doi:http://dx.doi.org/10.17632/prk6fsn56y.1Licensing provisions: GPLv2Programming language: Fortran 2003Nature of problem: Previously, the time-dependent R-Matrix with Time-dependent (RMT) codes could only be used with atomic data from atomic physics codes which did not include spin–orbit effects. When we desire to include spin–orbit effects in a level resolved Time-dependent R-Matrix calculation, we must use a different atomic structure and integral package, such as the RMatrixI package. However, while the RMatrixI package is able to include spin–orbit effects, it was not previously compatible for use with RMT.Solution method: To enable compatibility between RMatrixI and RMT, we write an alternative to the Stg1 code within the RMatrixI package (titled BSplineStg1) that uses B-Spline techniques to create and describe continuum orbitals. The necessary one- and two-electron integrals for the remainder of the RMatrixI package are calculated using Gauss–Legendre integration. The remainder of the Breit–Pauli R-Matrix codes require no further modification.

Relativistic photoionization cross section calculations and resonance parameters for Mg-like Se XXIII

Photoionization cross sections of the ground state 2p63s2 (1S0) and the first three excited states 2p63s3p (3Po0,1,2) of Mg-like Se XXIII have been reported by employing the fully relativistic Dirac atomic R-matrix code (DARC). For construction of target wavefunctions, multiconfiguration Dirac-Fock calculations are performed for the lowest 21 fine structure energy levels belonging to 2p6nl (3 ≤ n ≤ 5) configurations. Our calculated target state energies of the core ion Se XXIV show close agreement with the energies tabulated in the NIST database. In order to assess the accuracy of our DARC results, photoionization cross section calculations of the ground state configuration have also been performed using the close-coupling Breit-Pauli R-matrix (BPRM) method. Our two independent calculations show a good agreement both in magnitude and resonant photoionization cross sections. The resonance energies (Er) and widths (Γ) of the 3pns (3P1,1P1), 3pnd (3D1, 3P1, 1P1), 3dnp (3D1, 3P1, 1P1) and 3dnf (3D1, 3P1, 1P1) series due to ejection of a 3s electron from the ground state 2p63s2 (1S0) have also been predicted by adopting Quigley and Berrington (QB) method. We believe that our results might be beneficial for the modelling and diagnostics of fusion and laser generated plasmas.

Absolute single photoionization cross-sections of Br3+: experiment and theory

Absolute single photoionization cross section measurements for Br3+ ions are reported in the photon energy range 44.79–59.54 eV at a photon energy resolution of 21 ± 3 meV. Measurements were performed at the Advanced Light Source at Lawrence Berkeley National Laboratory using the merged-beams technique. Numerous resonance features in the experimental spectrum are assigned and their energies and quantum defect values are tabulated. The cross-section measurements are also compared with Breit–Pauli R-matrix calculations with suitable agreement over the photon energy range investigated. Analysis of the measured spectrum including Rydberg resonance series identifications produced a new emperical determination of the ionizational potential of Br3+ of 46.977 ± 0.050 eV, which is 805 meV lower than the most recently published value of 47.782 eV. This disparity between our determination and the earlier published value is similar to an 843 meV shift in the accepted ionization potential published for iso-electronic Se2+ as part of this same research program.

Single-photon photoionization of oxygen-like Ne III

We offer a theoretical and experimental study of the single-photon photoionization of Ne III. The high photon flux and the high-resolution capabilities of the Advanced Light Source at the LBNL were employed to measure absolute photoionization cross sections. The resulting spectrum has been benchmarked against high accuracy relativistic Breit-Pauli R-matrix calculations. A large close-coupling wave function expansion which comprises up to 58 fine-structure levels of the residual ion Ne IV of configurations 2s22p3, 2s2p4, 2p5, 2s22p23s, 2s22p23p and 2s22p23d was included. A complete identification of the measured features was achieved by considering seven low-lying levels of Ne III. We found that the photoionization cross-section (σPI) exhibits the presence of prominent resonances in the low-energy region near the ionization thresholds that correspond to low-lying levels. These include high-peak narrow resonances with almost zero background introduced by relativistic effects. However, there does not exist a significant contribution to σPI from relativistic effects at the high-energy interval of the present study.

Relativistic R-matrix calculations of photoionization cross sections of Cu XVIII

The total photoionization cross sections for the ground state 2p63s2(1S0) and the lowest three excited states 2p63s3p(3Po0,1,2) of the Mg-like Cu XVIII ion have been calculated by making use of the close-coupling Breit Pauli R-matrix (BPRM) approximation. The lowest 21 target level states of Cu XIX have been included in the photoionization calculations of Cu XVIII. Our calculated target state energies of the core ion Cu XIX show a good agreement with the observed energies tabulated in the NIST database. To further assess the accuracy of our BPRM results, photoionization cross section calculations for the ground state configuration have also been performed by employing the fully relativistic Dirac atomic R-matrix code (DARC). Our two independent calculations show a reasonable agreement between the calculated cross sections in the overall background shape and magnitude. We believe that our cross section data may be beneficial for the modelling and diagnostics of astrophysical and laboratory plasmas.

Collision and Radiative Rates for Infrared to Extreme Ultraviolet Lines of S iii

Abstract Electron excitation collision strengths for a wide range of transitions giving rise to infrared, optical, ultraviolet, and extreme ultraviolet lines of S iii have been calculated using the B-spline Breit–Pauli R-matrix method. The term-dependent non-orthogonal orbitals have been employed for the accurate representation of target wave functions and the electron plus S iii target scattering system. The multiconfiguration Hartree–Fock method has been utilized for the calculation of 198 S iii fine-structure level energies belonging to the , , , and 3s3p 25s configurations. The transition probabilities between fine-structure levels have also been calculated and compared with available other calculations. The close-coupling expansion includes these 198 fine-structure levels of S iii in the electron collision calculations. The effective collision strengths are calculated at electron temperatures in the range of 103–106 K for all possible transitions between the 198 fine-structure levels. The present calculation includes a larger number of levels in the close-coupling expansion and improved target description than previous calculations and should be useful for the analysis of measured spectra from various astrophysical objects. Comparison with other calculations is used to assess likely uncertainties in the existing collision and radiative rates for S iii. The collision and radiative rates are estimated to be accurate to about 20% or better for most main transitions of astrophysical importance.